Maintenance optimization for a system with an implemented interval of replacement activities

Most research on maintenance optimization regarded that a replacement activity is performed as soon as a planned time reaches, some other considered a time delay on replacement schedule when one job is completed or a failure comes. However, there is no existing research taking into account the influence of changes of the replacement schedule and catastrophic failures of a system on the replacement activity. In this paper, Failures of the system are divided into minor and catastrophic ones, and the replacement activity is performed either at the time when a catastrophic failure happens or in the implemented interval of the replacement activity randomly, whichever comes first. The objective of this paper is to find a constraint on the implemented interval length which is determined by engineers and an optimal implemented range of replacement activities for minimize the mean maintenance cost.